text: // This file is part of Eigen, a lightweight C++ template library
  // for linear algebra.
  //
  // Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
  //
  // This Source Code Form is subject to the terms of the Mozilla
  // Public License v. 2.0. If a copy of the MPL was not distributed
  // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
  
  #ifndef EIGEN_ALIGNEDBOX_H
  #define EIGEN_ALIGNEDBOX_H
  
  namespace Eigen { 
  
  /** \geometry_module \ingroup Geometry_Module
    *
    *
    * \class AlignedBox
    *
    * \brief An axis aligned box
    *
    * \param _Scalar the type of the scalar coefficients
    * \param _AmbientDim the dimension of the ambient space, can be a compile time value or Dynamic.
    *
    * This class represents an axis aligned box as a pair of the minimal and maximal corners.
    */
  template <typename _Scalar, int _AmbientDim>
  class AlignedBox
  {
  public:
  EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim)
    enum { AmbientDimAtCompileTime = _AmbientDim };
    typedef _Scalar                                   Scalar;
    typedef NumTraits<Scalar>                         ScalarTraits;
    typedef Eigen::Index                              Index; ///< \deprecated since Eigen 3.3
    typedef typename ScalarTraits::Real               RealScalar;
    typedef typename ScalarTraits::NonInteger      NonInteger;
    typedef Matrix<Scalar,AmbientDimAtCompileTime,1>  VectorType;
  
    /** Define constants to name the corners of a 1D, 2D or 3D axis aligned bounding box */
    enum CornerType
    {
      /** 1D names */
      Min=0, Max=1,
  
      /** Added names for 2D */
      BottomLeft=0, BottomRight=1,
      TopLeft=2, TopRight=3,
  
      /** Added names for 3D */
      BottomLeftFloor=0, BottomRightFloor=1,
      TopLeftFloor=2, TopRightFloor=3,
      BottomLeftCeil=4, BottomRightCeil=5,
      TopLeftCeil=6, TopRightCeil=7
    };
  
  
    /** Default constructor initializing a null box. */
    inline AlignedBox()
    { if (AmbientDimAtCompileTime!=Dynamic) setEmpty(); }
  
    /** Constructs a null box with \a _dim the dimension of the ambient space. */
    inline explicit AlignedBox(Index _dim) : m_min(_dim), m_max(_dim)
    { setEmpty(); }
  
    /** Constructs a box with extremities \a _min and \a _max. */
    template<typename OtherVectorType1, typename OtherVectorType2>
    inline AlignedBox(const OtherVectorType1& _min, const OtherVectorType2& _max) : m_min(_min), m_max(_max) {}
  
    /** Constructs a box containing a single point \a p. */
    template<typename Derived>
    inline explicit AlignedBox(const MatrixBase<Derived>& a_p)
    {
      typename internal::nested_eval<Derived,2>::type p(a_p.derived());
      m_min = p;
      m_max = p;
    }
  
    ~AlignedBox() {}
  
    /** \returns the dimension in which the box holds */
    inline Index dim() const { return AmbientDimAtCompileTime==Dynamic ? m_min.size() : Index(AmbientDimAtCompileTime); }
  
    /** \deprecated use isEmpty */
    inline bool isNull() const { return isEmpty(); }
  
    /** \deprecated use setEmpty */
    inline void setNull() { setEmpty(); }
  
    /** \returns true if the box is empty. */
    inline bool isEmpty() const { return (m_min.array() > m_max.array()).any(); }
  
    /** Makes \c *this an empty box. */
    inline void setEmpty()
    {
      m_min.setConstant( ScalarTraits::highest() );
      m_max.setConstant( ScalarTraits::lowest() );
    }
  
    /** \returns the minimal corner */
    inline const VectorType& (min)() const { return m_min; }
    /** \returns a non const reference to the minimal corner */
    inline VectorType& (min)() { return m_min; }
    /** \returns the maximal corner */
    inline const VectorType& (max)() const { return m_max; }
    /** \returns a non const reference to the maximal corner */
    inline VectorType& (max)() { return m_max; }
  
    /** \returns the center of the box */
    inline const CwiseUnaryOp<internal::scalar_quotient1_op<Scalar>,
                              const CwiseBinaryOp<internal::scalar_sum_op<Scalar>, const VectorType, const VectorType> >
    center() const
    { return (m_min+m_max)/2; }
  
    /** \returns the lengths of the sides of the bounding box.
      * Note that this function does not get the same
      * result for integral or floating scalar types: see
      */
    inline const CwiseBinaryOp< internal::scalar_difference_op<Scalar>, const VectorType, const VectorType> sizes() const
    { return m_max - m_min; }
  
    /** \returns the volume of the bounding box */
    inline Scalar volume() const
    { return sizes().prod(); }
  
    /** \returns an expression for the bounding box diagonal vector
      * if the length of the diagonal is needed: diagonal().norm()
      * will provide it.
      */
    inline CwiseBinaryOp< internal::scalar_difference_op<Scalar>, const VectorType, const VectorType> diagonal() const
    { return sizes(); }
  
    /** \returns the vertex of the bounding box at the corner defined by
      * the corner-id corner. It works only for a 1D, 2D or 3D bounding box.
      * For 1D bounding boxes corners are named by 2 enum constants:
      * BottomLeft and BottomRight.
      * For 2D bounding boxes, corners are named by 4 enum constants:
      * BottomLeft, BottomRight, TopLeft, TopRight.
      * For 3D bounding boxes, the following names are added:
      * BottomLeftCeil, BottomRightCeil, TopLeftCeil, TopRightCeil.
      */
    inline VectorType corner(CornerType corner) const
    {
      EIGEN_STATIC_ASSERT(_AmbientDim <= 3, THIS_METHOD_IS_ONLY_FOR_VECTORS_OF_A_SPECIFIC_SIZE);
  
      VectorType res;
  
      Index mult = 1;
      for(Index d=0; d<dim(); ++d)
      {
        if( mult & corner ) res[d] = m_max[d];
        else                res[d] = m_min[d];
        mult *= 2;
      }
      return res;
    }
  
    /** \returns a random point inside the bounding box sampled with
     * a uniform distribution */
    inline VectorType sample() const
    {
      VectorType r;
      for(Index d=0; d<dim(); ++d)
      {
        if(!ScalarTraits::IsInteger)
        {
          r[d] = m_min[d] + (m_max[d]-m_min[d])
               * internal::random<Scalar>(Scalar(0), Scalar(1));
        }
        else
          r[d] = internal::random(m_min[d], m_max[d]);
      }
      return r;
    }
  
    /** \returns true if the point \a p is inside the box \c *this. */
    template<typename Derived>
    inline bool contains(const MatrixBase<Derived>& a_p) const
    {
      typename internal::nested<Derived,2>::type p(a_p.derived());
      return (m_min.array()<=p.array()).all() && (p.array()<=m_max.array()).all();
    }
  
    /** \returns true if the box \a b is entirely inside the box \c *this. */
    inline bool contains(const AlignedBox& b) const
    { return (m_min.array()<=(b.min)().array()).all() && ((b.max)().array()<=m_max.array()).all(); }
  
    /** \returns true if the box \a b is intersecting the box \c *this. */
    inline bool intersects(const AlignedBox& b) const
    { return (m_min.array()<=(b.max)().array()).all() && ((b.min)().array()<=m_max.array()).all(); }
  
    /** Extends \c *this such that it contains the point \a p and returns a reference to \c *this. */
    template<typename Derived>
    inline AlignedBox& extend(const MatrixBase<Derived>& a_p)
    {
      typename internal::nested<Derived,2>::type p(a_p.derived());
      m_min = m_min.cwiseMin(p);
      m_max = m_max.cwiseMax(p);
      return *this;
    }
  
    /** Extends \c *this such that it contains the box \a b and returns a reference to \c *this. */
    inline AlignedBox& extend(const AlignedBox& b)
    {
      m_min = m_min.cwiseMin(b.m_min);
      m_max = m_max.cwiseMax(b.m_max);
      return *this;
    }
  
    /** Clamps \c *this by the box \a b and returns a reference to \c *this. */
    inline AlignedBox& clamp(const AlignedBox& b)
    {
      m_min = m_min.cwiseMax(b.m_min);
      m_max = m_max.cwiseMin(b.m_max);
      return *this;
    }
  
    /** Returns an AlignedBox that is the intersection of \a b and \c *this */
    inline AlignedBox intersection(const AlignedBox& b) const
    {return AlignedBox(m_min.cwiseMax(b.m_min), m_max.cwiseMin(b.m_max)); }
  
    /** Returns an AlignedBox that is the union of \a b and \c *this */
    inline AlignedBox merged(const AlignedBox& b) const
    { return AlignedBox(m_min.cwiseMin(b.m_min), m_max.cwiseMax(b.m_max)); }
  
    /** Translate \c *this by the vector \a t and returns a reference to \c *this. */
    template<typename Derived>
    inline AlignedBox& translate(const MatrixBase<Derived>& a_t)
    {
      const typename internal::nested<Derived,2>::type t(a_t.derived());
      m_min += t;
      m_max += t;
      return *this;
    }
  
    /** \returns the squared distance between the point \a p and the box \c *this,
      * and zero if \a p is inside the box.
      * \sa exteriorDistance()
      */
    template<typename Derived>
    inline Scalar squaredExteriorDistance(const MatrixBase<Derived>& a_p) const;
  
    /** \returns the squared distance between the boxes \a b and \c *this,
      * and zero if the boxes intersect.
      * \sa exteriorDistance()
      */
    inline Scalar squaredExteriorDistance(const AlignedBox& b) const;
  
    /** \returns the distance between the point \a p and the box \c *this,
      * and zero if \a p is inside the box.
      * \sa squaredExteriorDistance()
      */
    template<typename Derived>
    inline NonInteger exteriorDistance(const MatrixBase<Derived>& p) const
    { using std::sqrt; return sqrt(NonInteger(squaredExteriorDistance(p))); }
  
    /** \returns the distance between the boxes \a b and \c *this,
      * and zero if the boxes intersect.
      * \sa squaredExteriorDistance()
      */
    inline NonInteger exteriorDistance(const AlignedBox& b) const
    { using std::sqrt; return sqrt(NonInteger(squaredExteriorDistance(b))); }
  
    /** \returns \c *this with scalar type casted to \a NewScalarType
      *
      * Note that if \a NewScalarType is equal to the current scalar type of \c *this
      * then this function smartly returns a const reference to \c *this.
      */
    template<typename NewScalarType>
    inline typename internal::cast_return_type<AlignedBox,
             AlignedBox<NewScalarType,AmbientDimAtCompileTime> >::type cast() const
    {
      return typename internal::cast_return_type<AlignedBox,
                      AlignedBox<NewScalarType,AmbientDimAtCompileTime> >::type(*this);
    }
  
    /** Copy constructor with scalar type conversion */
    template<typename OtherScalarType>
    inline explicit AlignedBox(const AlignedBox<OtherScalarType,AmbientDimAtCompileTime>& other)
    {
      m_min = (other.min)().template cast<Scalar>();
      m_max = (other.max)().template cast<Scalar>();
    }
  
    /** \returns \c true if \c *this is approximately equal to \a other, within the precision
      * determined by \a prec.
      *
      * \sa MatrixBase::isApprox() */
    bool isApprox(const AlignedBox& other, const RealScalar& prec = ScalarTraits::dummy_precision()) const
    { return m_min.isApprox(other.m_min, prec) && m_max.isApprox(other.m_max, prec); }
  
  protected:
  
    VectorType m_min, m_max;
  };
  
  
  
  template<typename Scalar,int AmbientDim>
  template<typename Derived>
  inline Scalar AlignedBox<Scalar,AmbientDim>::squaredExteriorDistance(const MatrixBase<Derived>& a_p) const
  {
    typename internal::nested<Derived,2*AmbientDim>::type p(a_p.derived());
    Scalar dist2(0);
    Scalar aux;
    for (Index k=0; k<dim(); ++k)
    {
      if( m_min[k] > p[k] )
      {
        aux = m_min[k] - p[k];
        dist2 += aux*aux;
      }
      else if( p[k] > m_max[k] )
      {
        aux = p[k] - m_max[k];
        dist2 += aux*aux;
      }
    }
    return dist2;
  }
  
  template<typename Scalar,int AmbientDim>
  inline Scalar AlignedBox<Scalar,AmbientDim>::squaredExteriorDistance(const AlignedBox& b) const
  {
    Scalar dist2(0);
    Scalar aux;
    for (Index k=0; k<dim(); ++k)
    {
      if( m_min[k] > b.m_max[k] )
      {
        aux = m_min[k] - b.m_max[k];
        dist2 += aux*aux;
      }
      else if( b.m_min[k] > m_max[k] )
      {
        aux = b.m_min[k] - m_max[k];
        dist2 += aux*aux;
      }
    }
    return dist2;
  }
  
  /** \defgroup alignedboxtypedefs Global aligned box typedefs
    *
    * \ingroup Geometry_Module
    *
    * Eigen defines several typedef shortcuts for most common aligned box types.
    *
    * The general patterns are the following:
    *
    * \c AlignedBoxSizeType where \c Size can be \c 1, \c 2,\c 3,\c 4 for fixed size boxes or \c X for dynamic size,
    * and where \c Type can be \c i for integer, \c f for float, \c d for double.
    *
    * For example, \c AlignedBox3d is a fixed-size 3x3 aligned box type of doubles, and \c AlignedBoxXf is a dynamic-size aligned box of floats.
    *
    * \sa class AlignedBox
    */
  
  #define EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Size, SizeSuffix)    \
  /** \ingroup alignedboxtypedefs */                                 \
  typedef AlignedBox<Type, Size>   AlignedBox##SizeSuffix##TypeSuffix;
  
  #define EIGEN_MAKE_TYPEDEFS_ALL_SIZES(Type, TypeSuffix) \
  EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 1, 1) \
  EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 2, 2) \
  EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 3, 3) \
  EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 4, 4) \
  EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Dynamic, X)
  
  EIGEN_MAKE_TYPEDEFS_ALL_SIZES(int,                  i)
  EIGEN_MAKE_TYPEDEFS_ALL_SIZES(float,                f)
  EIGEN_MAKE_TYPEDEFS_ALL_SIZES(double,               d)
  
  #undef EIGEN_MAKE_TYPEDEFS_ALL_SIZES
  #undef EIGEN_MAKE_TYPEDEFS
  
  } // end namespace Eigen
  
  #endif // EIGEN_ALIGNEDBOX_H
  